(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "), analytic_val_y : exact_soln_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%o3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "), analytic_val_y : exact_soln_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%i4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%o4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((!array_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! >
! 1, n!
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (!array_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
1, 1
array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
2, 1
array_complex_pole : ord_no), found : false,
2, 2
if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((!array_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! >
! 1, n!
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (!array_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
1, 1
array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
2, 1
array_complex_pole : ord_no), found : false,
2, 2
if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%i7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii))
iii ! iii!
(%o7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_y2_higher ,
1 6, 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp2 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp4 : array_y1 - array_const_2D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp4 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_y2_higher , array_tmp2 :
2 6, 2 2
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(1, 2), array_y1 : temporary,
2 3
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y1_higher : temporary)), kkk : 3,
2, 2
array_tmp4 : array_y1 - array_const_2D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp4 glob_h factorial_3(1, 2),
2
array_y2 : temporary, array_y2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_y2_higher , array_tmp2 :
3 6, 3 3
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(2, 3), array_y1 : temporary,
3 4
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y1_higher : temporary)), kkk : 4,
2, 3
array_tmp4 : array_y1 - array_const_2D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp4 glob_h factorial_3(2, 3),
3
array_y2 : temporary, array_y2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_y2_higher , array_tmp2 :
4 6, 4 4
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(3, 4), array_y1 : temporary,
4 5
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y1_higher : temporary)), kkk : 5,
2, 4
array_tmp4 : array_y1 - array_const_2D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp4 glob_h factorial_3(3, 4),
4
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_y2_higher , array_tmp2 :
5 6, 5 5
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(4, 5), array_y1 : temporary,
5 6
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y1_higher : temporary)), kkk : 6,
2, 5
array_tmp4 : array_y1 - array_const_2D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp4 glob_h factorial_3(4, 5),
5
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y2_higher ,
kkk 6, kkk
array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp4 :
kkk
array_y1 - array_const_2D0 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
2, order_d + kkk
order_d
array_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_y2_higher ,
1 6, 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp2 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp4 : array_y1 - array_const_2D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp4 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_y2_higher , array_tmp2 :
2 6, 2 2
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(1, 2), array_y1 : temporary,
2 3
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y1_higher : temporary)), kkk : 3,
2, 2
array_tmp4 : array_y1 - array_const_2D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp4 glob_h factorial_3(1, 2),
2
array_y2 : temporary, array_y2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_y2_higher , array_tmp2 :
3 6, 3 3
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(2, 3), array_y1 : temporary,
3 4
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y1_higher : temporary)), kkk : 4,
2, 3
array_tmp4 : array_y1 - array_const_2D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp4 glob_h factorial_3(2, 3),
3
array_y2 : temporary, array_y2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_y2_higher , array_tmp2 :
4 6, 4 4
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(3, 4), array_y1 : temporary,
4 5
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y1_higher : temporary)), kkk : 5,
2, 4
array_tmp4 : array_y1 - array_const_2D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp4 glob_h factorial_3(3, 4),
4
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_y2_higher , array_tmp2 :
5 6, 5 5
array_tmp1 + array_const_0D0 , if not array_y1_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(4, 5), array_y1 : temporary,
5 6
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y1_higher : temporary)), kkk : 6,
2, 5
array_tmp4 : array_y1 - array_const_2D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp4 glob_h factorial_3(4, 5),
5
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y2_higher ,
kkk 6, kkk
array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp4 :
kkk
array_y1 - array_const_2D0 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
2, order_d + kkk
order_d
array_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
log(x)
(%i9) log10(x) := ---------
log(10.0)
log(x)
(%o9) log10(x) := ---------
log(10.0)
(%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, "
"),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i21) mode_declare(ats, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o21) [ats]
(%i22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i23) mode_declare(att, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o23) [att]
(%i24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i35) mode_declare(comp_expect_sec, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o35) [comp_expect_sec]
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) mode_declare(comp_percent, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o37) [comp_percent]
(%i38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i39) mode_declare(factorial_1, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o39) [factorial_1]
(%i40) factorial_1(nnn) := nnn!
(%o40) factorial_1(nnn) := nnn!
(%i41) mode_declare(factorial_3, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o41) [factorial_3]
mmm2!
(%i42) factorial_3(mmm2, nnn2) := -----
nnn2!
mmm2!
(%o42) factorial_3(mmm2, nnn2) := -----
nnn2!
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) exact_soln_y1(x) := sin(x) + 2.0
(%o49) exact_soln_y1(x) := sin(x) + 2.0
(%i50) exact_soln_y2(x) := 2.0 - cos(x)
(%o50) exact_soln_y2(x) := 2.0 - cos(x)
(%i51) exact_soln_y2p(x) := sin(x)
(%o51) exact_soln_y2p(x) := sin(x)
(%i52) exact_soln_y2pp(x) := cos(x)
(%o52) exact_soln_y2pp(x) := cos(x)
(%i53) exact_soln_y2ppp(x) := - sin(x)
(%o53) exact_soln_y2ppp(x) := - sin(x)
(%i54) exact_soln_y2pppp(x) := - cos(x)
(%o54) exact_soln_y2pppp(x) := - cos(x)
(%i55) mainprog() := (define_variable(ALWAYS, 1, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_h, 0.1, float), define_variable(glob_hmin, 1.0E-11,
float), define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/mtest9postode.ode#################"),
omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"),
omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.5,"), omniout_str(ALWAYS, "x_end : 10.0,"),
omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"),
omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"),
omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"),
omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10,"),
omniout_str(ALWAYS, "glob_subiter_method : 3,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "2.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2p (x) := ("),
omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("),
omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("),
omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_y2, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y1_init, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_y2_higher_work, 1 + 6, 1 + max_terms),
array(array_y2_higher_work2, 1 + 6, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work, 1 + 2,
1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y2_higher, 1 + 6, 1 + max_terms),
array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), term : 1,
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y2_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), ord : 1,
term
while ord <= 6 do (term : 1, while term <=
max_terms do (array_y2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_5, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term),
term
array_const_5 : 5, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, x_start : 0.5, x_end : 10.0,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start),
1 + 0
array_y2_init : exact_soln_y2p(x_start),
1 + 1
array_y2_init : exact_soln_y2pp(x_start),
1 + 2
array_y2_init : exact_soln_y2ppp(x_start),
1 + 3
array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5,
1 + 4
glob_look_poles : true, glob_max_iter : 10, glob_subiter_method : 3,
glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100,
glob_max_minutes : 15, glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y1_set_initial : true, array_y1_set_initial : false,
1, 1 1, 2
array_y1_set_initial : false, array_y1_set_initial : false,
1, 3 1, 4
array_y1_set_initial : false, array_y1_set_initial : false,
1, 5 1, 6
array_y1_set_initial : false, array_y1_set_initial : false,
1, 7 1, 8
array_y1_set_initial : false, array_y1_set_initial : false,
1, 9 1, 10
array_y1_set_initial : false, array_y1_set_initial : false,
1, 11 1, 12
array_y1_set_initial : false, array_y1_set_initial : false,
1, 13 1, 14
array_y1_set_initial : false, array_y1_set_initial : false,
1, 15 1, 16
array_y1_set_initial : false, array_y1_set_initial : false,
1, 17 1, 18
array_y1_set_initial : false, array_y1_set_initial : false,
1, 19 1, 20
array_y1_set_initial : false, array_y1_set_initial : false,
1, 21 1, 22
array_y1_set_initial : false, array_y1_set_initial : false,
1, 23 1, 24
array_y1_set_initial : false, array_y1_set_initial : false,
1, 25 1, 26
array_y1_set_initial : false, array_y1_set_initial : false,
1, 27 1, 28
array_y1_set_initial : false, array_y1_set_initial : false,
1, 29 1, 30
array_y2_set_initial : true, array_y2_set_initial : true,
2, 1 2, 2
array_y2_set_initial : true, array_y2_set_initial : true,
2, 3 2, 4
array_y2_set_initial : true, array_y2_set_initial : false,
2, 5 2, 6
array_y2_set_initial : false, array_y2_set_initial : false,
2, 7 2, 8
array_y2_set_initial : false, array_y2_set_initial : false,
2, 9 2, 10
array_y2_set_initial : false, array_y2_set_initial : false,
2, 11 2, 12
array_y2_set_initial : false, array_y2_set_initial : false,
2, 13 2, 14
array_y2_set_initial : false, array_y2_set_initial : false,
2, 15 2, 16
array_y2_set_initial : false, array_y2_set_initial : false,
2, 17 2, 18
array_y2_set_initial : false, array_y2_set_initial : false,
2, 19 2, 20
array_y2_set_initial : false, array_y2_set_initial : false,
2, 21 2, 22
array_y2_set_initial : false, array_y2_set_initial : false,
2, 23 2, 24
array_y2_set_initial : false, array_y2_set_initial : false,
2, 25 2, 26
array_y2_set_initial : false, array_y2_set_initial : false,
2, 27 2, 28
array_y2_set_initial : false, array_y2_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y1_init glob_h
it
array_y1_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 5, term_no : 1,
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (omniout_str
(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
2, iii
array_y1_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 5, ord : 6, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y2_higher_work :
6, iii
array_y2_higher
6, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 6, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 6, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 6, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"),
omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T03:46:11-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest9"),
logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest9 diffeq.max"), logitem_str(html_log_file, "\
mtest9 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff(y2,x,1) = y1 - 2.0;"), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ),
2
logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file),
2
logitem_pole(html_log_file, array_type_pole ),
2
if (array_type_pole = 1) or (array_type_pole = 2)
2 2
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logditto(html_log_file), if glob_percent_done < 100.0
then (logditto(html_log_file), 0) else (logditto(html_log_file), 0),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o55) mainprog() := (define_variable(ALWAYS, 1, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_h, 0.1, float), define_variable(glob_hmin, 1.0E-11,
float), define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/mtest9postode.ode#################"),
omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"),
omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.5,"), omniout_str(ALWAYS, "x_end : 10.0,"),
omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"),
omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"),
omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"),
omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10,"),
omniout_str(ALWAYS, "glob_subiter_method : 3,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "2.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2p (x) := ("),
omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("),
omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("),
omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_y2, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y1_init, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_y2_higher_work, 1 + 6, 1 + max_terms),
array(array_y2_higher_work2, 1 + 6, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work, 1 + 2,
1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y2_higher, 1 + 6, 1 + max_terms),
array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), term : 1,
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y2_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), ord : 1,
term
while ord <= 6 do (term : 1, while term <=
max_terms do (array_y2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_5, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term),
term
array_const_5 : 5, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, x_start : 0.5, x_end : 10.0,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start),
1 + 0
array_y2_init : exact_soln_y2p(x_start),
1 + 1
array_y2_init : exact_soln_y2pp(x_start),
1 + 2
array_y2_init : exact_soln_y2ppp(x_start),
1 + 3
array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5,
1 + 4
glob_look_poles : true, glob_max_iter : 10, glob_subiter_method : 3,
glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100,
glob_max_minutes : 15, glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y1_set_initial : true, array_y1_set_initial : false,
1, 1 1, 2
array_y1_set_initial : false, array_y1_set_initial : false,
1, 3 1, 4
array_y1_set_initial : false, array_y1_set_initial : false,
1, 5 1, 6
array_y1_set_initial : false, array_y1_set_initial : false,
1, 7 1, 8
array_y1_set_initial : false, array_y1_set_initial : false,
1, 9 1, 10
array_y1_set_initial : false, array_y1_set_initial : false,
1, 11 1, 12
array_y1_set_initial : false, array_y1_set_initial : false,
1, 13 1, 14
array_y1_set_initial : false, array_y1_set_initial : false,
1, 15 1, 16
array_y1_set_initial : false, array_y1_set_initial : false,
1, 17 1, 18
array_y1_set_initial : false, array_y1_set_initial : false,
1, 19 1, 20
array_y1_set_initial : false, array_y1_set_initial : false,
1, 21 1, 22
array_y1_set_initial : false, array_y1_set_initial : false,
1, 23 1, 24
array_y1_set_initial : false, array_y1_set_initial : false,
1, 25 1, 26
array_y1_set_initial : false, array_y1_set_initial : false,
1, 27 1, 28
array_y1_set_initial : false, array_y1_set_initial : false,
1, 29 1, 30
array_y2_set_initial : true, array_y2_set_initial : true,
2, 1 2, 2
array_y2_set_initial : true, array_y2_set_initial : true,
2, 3 2, 4
array_y2_set_initial : true, array_y2_set_initial : false,
2, 5 2, 6
array_y2_set_initial : false, array_y2_set_initial : false,
2, 7 2, 8
array_y2_set_initial : false, array_y2_set_initial : false,
2, 9 2, 10
array_y2_set_initial : false, array_y2_set_initial : false,
2, 11 2, 12
array_y2_set_initial : false, array_y2_set_initial : false,
2, 13 2, 14
array_y2_set_initial : false, array_y2_set_initial : false,
2, 15 2, 16
array_y2_set_initial : false, array_y2_set_initial : false,
2, 17 2, 18
array_y2_set_initial : false, array_y2_set_initial : false,
2, 19 2, 20
array_y2_set_initial : false, array_y2_set_initial : false,
2, 21 2, 22
array_y2_set_initial : false, array_y2_set_initial : false,
2, 23 2, 24
array_y2_set_initial : false, array_y2_set_initial : false,
2, 25 2, 26
array_y2_set_initial : false, array_y2_set_initial : false,
2, 27 2, 28
array_y2_set_initial : false, array_y2_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y1_init glob_h
it
array_y1_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 5, term_no : 1,
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (omniout_str
(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
2, iii
array_y1_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 5, ord : 6, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y2_higher_work :
6, iii
array_y2_higher
6, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 6, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 6, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 6, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"),
omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T03:46:11-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest9"),
logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest9 diffeq.max"), logitem_str(html_log_file, "\
mtest9 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff(y2,x,1) = y1 - 2.0;"), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ),
2
logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file),
2
logitem_pole(html_log_file, array_type_pole ),
2
if (array_type_pole = 1) or (array_type_pole = 2)
2 2
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logditto(html_log_file), if glob_percent_done < 100.0
then (logditto(html_log_file), 0) else (logditto(html_log_file), 0),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i56) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest9postode.ode#################"
"diff(y1,x,1) = diff(y2,x,5);"
"diff(y2,x,1) = y1 - 2.0;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.5,"
"x_end : 10.0,"
"array_y1_init[0 + 1] : exact_soln_y1(x_start),"
"array_y2_init[0 + 1] : exact_soln_y2(x_start),"
"array_y2_init[1 + 1] : exact_soln_y2p(x_start),"
"array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"
"array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"
"array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"
"glob_h : 0.00001 ,"
"glob_look_poles : true,"
"glob_max_iter : 10,"
"glob_subiter_method : 3,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.0001 ,"
"glob_look_poles : true,"
"glob_max_iter : 100,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y1 (x) := ("
"2.0 + sin(x) "
");"
"exact_soln_y2 (x) := ("
"2.0 - cos(x) "
");"
"exact_soln_y2p (x) := ("
"sin(x) "
");"
"exact_soln_y2pp (x) := ("
"cos(x) "
");"
"exact_soln_y2ppp (x) := ("
"-sin(x) "
");"
"exact_soln_y2pppp (x) := ("
"-cos(x) "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.5 " "
y1[1] (analytic) = 2.479425538604203 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1224174381096272 " "
y2[1] (numeric) = 1.1224174381096272 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
x[1] = 0.5 " "
y1[1] (analytic) = 2.479425538604203 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1224174381096272 " "
y2[1] (numeric) = 1.1224174381096272 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5001 " "
y1[1] (analytic) = 2.479513294463118 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.77558589151838900000E-5 " "
relative error = 3.539237281411125000E-3 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1224653850513207 " "
y2[1] (numeric) = 1.1224653850513207 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5002 " "
y1[1] (analytic) = 2.4796010455269 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.75506922697188370000E-4 " "
relative error = 7.078030678112343000E-3 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.12251334076836 " "
y2[1] (numeric) = 1.12251334076836 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5003 " "
y1[1] (analytic) = 2.479688791794672 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.63253190468937250000E-4 " "
relative error = 1.061638022239105600E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.122561305260266 " "
y2[1] (numeric) = 1.122561305260266 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5004 " "
y1[1] (analytic) = 2.4797765332655555 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.50994661352466150000E-4 " "
relative error = 1.415428594649414400E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1226092785265591 " "
y2[1] (numeric) = 1.1226092785265591 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5005 " "
y1[1] (analytic) = 2.479864269938674 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.387313344711430000E-4 " "
relative error = 1.769174788271749300E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1226572605667593 " "
y2[1] (numeric) = 1.1226572605667593 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5005999999999999 " "
y1[1] (analytic) = 2.47995200181315 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.2646320894700340000E-4 " "
relative error = 2.122876606329856500E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.122705251380387 " "
y2[1] (numeric) = 1.1227052513803868 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.977764018223156200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5006999999999999 " "
y1[1] (analytic) = 2.4800397288881055 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.1419028390252710000E-4 " "
relative error = 2.476534052048801300E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1227532509669618 " "
y2[1] (numeric) = 1.1227532509669618 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5007999999999999 " "
y1[1] (analytic) = 2.480127451162664 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.0191255846108190000E-4 " "
relative error = 2.830147128656758700E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1228012593260046 " "
y2[1] (numeric) = 1.1228012593260044 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.977594904536536500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5008999999999999 " "
y1[1] (analytic) = 2.480215168635948 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.8963003174514770000E-4 " "
relative error = 3.183715839377851400E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1228492764570344 " "
y2[1] (numeric) = 1.1228492764570344 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5009999999999999 " "
y1[1] (analytic) = 2.48030288130708 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.7734270287720410000E-4 " "
relative error = 3.537240187435731000E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1228973023595716 " "
y2[1] (numeric) = 1.1228973023595716 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5010999999999999 " "
y1[1] (analytic) = 2.4803905891751836 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 9.650505709806190000E-4 " "
relative error = 3.89072017605715860E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1229453370331357 " "
y2[1] (numeric) = 1.1229453370331357 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5011999999999999 " "
y1[1] (analytic) = 2.4804782922393813 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.0527536351783162000E-3 " "
relative error = 4.24415580846663200E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1229933804772465 " "
y2[1] (numeric) = 1.1229933804772465 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5012999999999999 " "
y1[1] (analytic) = 2.480565990498796 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.1404518945927755000E-3 " "
relative error = 4.59754708788638900E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1230414326914233 " "
y2[1] (numeric) = 1.1230414326914235 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.977171976575170800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5013999999999998 " "
y1[1] (analytic) = 2.480653683952551 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.2281453483478089000E-3 " "
relative error = 4.950894017543564500E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.123089493675186 " "
y2[1] (numeric) = 1.123089493675186 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5014999999999998 " "
y1[1] (analytic) = 2.4807413725997685 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.3158339955654520000E-3 " "
relative error = 5.30419660065766400E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1231375634280538 " "
y2[1] (numeric) = 1.1231375634280538 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5015999999999998 " "
y1[1] (analytic) = 2.4808290564395725 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.4035178353695166000E-3 " "
relative error = 5.65745484045487700E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1231856419495458 " "
y2[1] (numeric) = 1.1231856419495458 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5016999999999998 " "
y1[1] (analytic) = 2.4809167354710864 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.4911968668833708000E-3 " "
relative error = 6.01066874015913500E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1232337292391814 " "
y2[1] (numeric) = 1.1232337292391814 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5017999999999998 " "
y1[1] (analytic) = 2.4810044096934325 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.5788710892294944000E-3 " "
relative error = 6.36383830299031600E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1232818252964796 " "
y2[1] (numeric) = 1.1232818252964798 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.976748843652168200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5018999999999998 " "
y1[1] (analytic) = 2.4810920791057347 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.6665405015316992000E-3 " "
relative error = 6.71696353217319500E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1233299301209596 " "
y2[1] (numeric) = 1.1233299301209598 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.976664192514853100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5019999999999998 " "
y1[1] (analytic) = 2.4811797437071164 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.7542051029133532000E-3 " "
relative error = 7.07004443093028700E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1233780437121403 " "
y2[1] (numeric) = 1.1233780437121406 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.976579533202351400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5020999999999998 " "
y1[1] (analytic) = 2.4812674034967 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.841864892496936000E-3 " "
relative error = 7.42308100248005300E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1234261660695406 " "
y2[1] (numeric) = 1.1234261660695408 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.97649486571854220000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5021999999999998 " "
y1[1] (analytic) = 2.48135505847361 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 1.929519869407148000E-3 " "
relative error = 7.77607325004943100E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1234742971926792 " "
y2[1] (numeric) = 1.1234742971926794 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.976410190067303400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5022999999999997 " "
y1[1] (analytic) = 2.4814427086369695 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.0171700327664688000E-3 " "
relative error = 8.1290211768559400E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1235224370810748 " "
y2[1] (numeric) = 1.123522437081075 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.976325506252513700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5023999999999997 " "
y1[1] (analytic) = 2.4815303539859017 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.1048153816987103000E-3 " "
relative error = 8.48192478612199300E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1235705857342462 " "
y2[1] (numeric) = 1.1235705857342462 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5024999999999997 " "
y1[1] (analytic) = 2.4816179945195302 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.1924559153272405000E-3 " "
relative error = 8.83478408106774400E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1236187431517117 " "
y2[1] (numeric) = 1.1236187431517115 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.976156114147792400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5025999999999997 " "
y1[1] (analytic) = 2.481705630236979 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.2800916327758713000E-3 " "
relative error = 9.1875990649146600E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1236669093329894 " "
y2[1] (numeric) = 1.1236669093329894 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5026999999999997 " "
y1[1] (analytic) = 2.4817932611373714 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.367722533168414900E-3 " "
relative error = 9.54036974088373600E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1237150842775985 " "
y2[1] (numeric) = 1.1237150842775983 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.975986689435399700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5027999999999997 " "
y1[1] (analytic) = 2.4818808872198312 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.455348615628239000E-3 " "
relative error = 9.89309611219371100E-2 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1237632679850564 " "
y2[1] (numeric) = 1.1237632679850562 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.975901964861019000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5028999999999997 " "
y1[1] (analytic) = 2.4819685084834826 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.5429698792795996000E-3 " "
relative error = 0.10245778182066419 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1238114604548817 " "
y2[1] (numeric) = 1.1238114604548815 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.975817232146351300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5029999999999997 " "
y1[1] (analytic) = 2.4820561249274484 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.6305863232454210000E-3 " "
relative error = 0.10598415953717863 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1238596616865926 " "
y2[1] (numeric) = 1.123859661686592 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.92719747388581600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5030999999999997 " "
y1[1] (analytic) = 2.482143736550853 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.7181979466499584000E-3 " "
relative error = 0.10951009430368938 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1239078716797066 " "
y2[1] (numeric) = 1.1239078716797057 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.90259096924663200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5031999999999996 " "
y1[1] (analytic) = 2.4822313433528205 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.8058047486174686000E-3 " "
relative error = 0.11303558615240063 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.123956090433742 " "
y2[1] (numeric) = 1.123956090433741 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.87781492599692500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5032999999999996 " "
y1[1] (analytic) = 2.4823189453324743 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.8934067282713194000E-3 " "
relative error = 0.11656063511547607 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1240043179482164 " "
y2[1] (numeric) = 1.124004317948215 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.1852869319773969000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5033999999999996 " "
y1[1] (analytic) = 2.4824065424889388 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 2.9810038847357667000E-3 " "
relative error = 0.12008524122511048 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1240525542226476 " "
y2[1] (numeric) = 1.124052554222646 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.3827754126230538000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5034999999999996 " "
y1[1] (analytic) = 2.4824941348213376 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.0685962171346226000E-3 " "
relative error = 0.12360940451347596 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1241007992565533 " "
y2[1] (numeric) = 1.1241007992565515 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.5802469321034910000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5035999999999996 " "
y1[1] (analytic) = 2.4825817223287956 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.1561837245925870000E-3 " "
relative error = 0.12713312501277568 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1241490530494511 " "
y2[1] (numeric) = 1.124149053049449 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.97522387554120550000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5036999999999996 " "
y1[1] (analytic) = 2.482669305010436 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.2437664062330285000E-3 " "
relative error = 0.13065640275515442 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1241973156008582 " "
y2[1] (numeric) = 1.1241973156008558 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.17265298562813960000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5037999999999996 " "
y1[1] (analytic) = 2.482756882865383 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.3313442611802024000E-3 " "
relative error = 0.134179237772788 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.124245586910292 " "
y2[1] (numeric) = 1.1242455869102894 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.37006512644909240000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5038999999999996 " "
y1[1] (analytic) = 2.482844455892762 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.4189172885588090000E-3 " "
relative error = 0.13770163009786537 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1242938669772704 " "
y2[1] (numeric) = 1.124293866977267 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.9624541872047810000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5039999999999996 " "
y1[1] (analytic) = 2.482932024091696 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.506485487493105000E-3 " "
relative error = 0.14122357976255287 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1243421558013098 " "
y2[1] (numeric) = 1.124342155801306 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.3573038814285960000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5040999999999995 " "
y1[1] (analytic) = 2.48301958746131 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.594048857106902000E-3 " "
relative error = 0.14474508679899425 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1243904533819276 " "
y2[1] (numeric) = 1.1243904533819233 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.7521196314733890000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5041999999999995 " "
y1[1] (analytic) = 2.4831071460007275 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.6816073965244556000E-3 " "
relative error = 0.14826615123934636 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.124438759718641 " "
y2[1] (numeric) = 1.124438759718636 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.3443729292763060000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5042999999999995 " "
y1[1] (analytic) = 2.4831946997090744 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.7691611048713547000E-3 " "
relative error = 0.15178677311581493 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1244870748109668 " "
y2[1] (numeric) = 1.1244870748109612 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.9365753039526566000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5043999999999995 " "
y1[1] (analytic) = 2.4832822485854735 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.856709981270523000E-3 " "
relative error = 0.1553069524604938 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1245353986584217 " "
y2[1] (numeric) = 1.1245353986584155 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.5287267482358460000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5044999999999995 " "
y1[1] (analytic) = 2.4833697926290506 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 3.944254024847549000E-3 " "
relative error = 0.15882668930557922 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1245837312605227 " "
y2[1] (numeric) = 1.1245837312605156 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.3182732953434020000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5045999999999995 " "
y1[1] (analytic) = 2.4834573318389297 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.031793234726688000E-3 " "
relative error = 0.16234598368320907 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1246320726167864 " "
y2[1] (numeric) = 1.1246320726167784 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.1077519234371990000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5046999999999995 " "
y1[1] (analytic) = 2.4835448662142356 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.1193276100326415000E-3 " "
relative error = 0.16586483562553445 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1246804227267293 " "
y2[1] (numeric) = 1.1246804227267204 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 7.897162622843410000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5047999999999995 " "
y1[1] (analytic) = 2.4836323957540927 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.2068571498896645000E-3 " "
relative error = 0.1693832451646838 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.124728781589868 " "
y2[1] (numeric) = 1.1247287815898581 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.883925960801090000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5048999999999995 " "
y1[1] (analytic) = 2.483719920457626 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.294381853422901700E-3 " "
relative error = 0.17290121233281652 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.124777149205719 " "
y2[1] (numeric) = 1.124777149205708 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.8706043718007590000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5049999999999994 " "
y1[1] (analytic) = 2.4838074403239596 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.381901719756609000E-3 " "
relative error = 0.17641873716205164 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1248255255737984 " "
y2[1] (numeric) = 1.124825525573786 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.105460144092893000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5050999999999994 " "
y1[1] (analytic) = 2.4838949553522194 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.469416748016375000E-3 " "
relative error = 0.1799358196845569 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1248739106936225 " "
y2[1] (numeric) = 1.1248739106936088 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2238496576796812000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5051999999999994 " "
y1[1] (analytic) = 2.483982465541529 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.556926937326011300E-3 " "
relative error = 0.183452459932424 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1249223045647074 " "
y2[1] (numeric) = 1.1249223045646923 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.342228976493159000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5052999999999994 " "
y1[1] (analytic) = 2.4840699708910146 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.644432286811550600E-3 " "
relative error = 0.18696865793782905 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1249707071865696 " "
y2[1] (numeric) = 1.1249707071865527 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.5000737233866213000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5053999999999994 " "
y1[1] (analytic) = 2.4841574713998003 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.731932795597249000E-3 " "
relative error = 0.1904844137328721 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1250191185587244 " "
y2[1] (numeric) = 1.125019118558706 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.6381679124162896000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5054999999999994 " "
y1[1] (analytic) = 2.4842449670670113 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.819428462808250700E-3 " "
relative error = 0.19399972734968407 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.125067538680688 " "
y2[1] (numeric) = 1.125067538680668 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.7959863166857085000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5055999999999994 " "
y1[1] (analytic) = 2.4843324578917723 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.906919287569256000E-3 " "
relative error = 0.1975145988203734 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1251159675519764 " "
y2[1] (numeric) = 1.1251159675519542 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.9735263859791735000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5056999999999994 " "
y1[1] (analytic) = 2.484419943873209 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 4.994405269005852700E-3 " "
relative error = 0.20102902817707938 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.125164405172105 " "
y2[1] (numeric) = 1.1251644051720808 " "
absolute error = 2.420286193682841300000000000000E-14 " "
relative error = 2.15105115533106000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5057999999999994 " "
y1[1] (analytic) = 2.484507425010446 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.081886406243186000E-3 " "
relative error = 0.20454301545191875 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1252128515405895 " "
y2[1] (numeric) = 1.1252128515405633 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 2.3285606225773312000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5058999999999994 " "
y1[1] (analytic) = 2.4845949013026094 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.169362698406399000E-3 " "
relative error = 0.2080565606770035 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1252613066569457 " "
y2[1] (numeric) = 1.125261306656917 " "
absolute error = 2.86437540353290400000000000000E-14 " "
relative error = 2.5455202152491285000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5059999999999993 " "
y1[1] (analytic) = 2.484682372748823 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.256834144620193000E-3 " "
relative error = 0.21156966388442305 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1253097705206885 " "
y2[1] (numeric) = 1.1253097705206574 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 2.7624611021657236000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5060999999999993 " "
y1[1] (analytic) = 2.4847698393482136 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.344300744010599000E-3 " "
relative error = 0.21508232510631556 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1253582431313336 " "
y2[1] (numeric) = 1.1253582431313 " "
absolute error = 3.35287353436797300000000000000E-14 " "
relative error = 2.9793832806862725000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5061999999999993 " "
y1[1] (analytic) = 2.4848573010999058 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.431762495702763000E-3 " "
relative error = 0.21859454437477877 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1254067244883965 " "
y2[1] (numeric) = 1.12540672448836 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 3.2357470783959750000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5062999999999993 " "
y1[1] (analytic) = 2.4849447580030244 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.5192193988213840000E-3 " "
relative error = 0.22210632172188782 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.125455214591392 " "
y2[1] (numeric) = 1.1254552145913526 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 3.511818077186229000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5063999999999993 " "
y1[1] (analytic) = 2.485032210056696 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.6066714524929400000E-3 " "
relative error = 0.22561765717978455 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1255037134398354 " "
y2[1] (numeric) = 1.1255037134397927 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.7878652585969425000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5064999999999993 " "
y1[1] (analytic) = 2.4851196572600447 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.6941186558416850000E-3 " "
relative error = 0.22912855078051672 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1255522210332418 " "
y2[1] (numeric) = 1.1255522210331954 " "
absolute error = 4.640732242933154300000000000000E-14 " "
relative error = 4.123071463244082000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5065999999999993 " "
y1[1] (analytic) = 2.4852070996121975 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.78156100799454000E-3 " "
relative error = 0.23263900255623443 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1256007373711259 " "
y2[1] (numeric) = 1.1256007373710757 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 4.458248741934802000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5066999999999993 " "
y1[1] (analytic) = 2.485294537112279 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.868998508076206000E-3 " "
relative error = 0.2361490125389939 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1256492624530026 " "
y2[1] (numeric) = 1.1256492624529484 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 4.8131230045530890000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5067999999999993 " "
y1[1] (analytic) = 2.4853819697594153 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 5.956431155212272000E-3 " "
relative error = 0.23965858076088215 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1256977962783865 " "
y2[1] (numeric) = 1.1256977962783283 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 5.16796663213608000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5068999999999992 " "
y1[1] (analytic) = 2.485469397552732 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.043858948529213000E-3 " "
relative error = 0.2431677072540172 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1257463388467925 " "
y2[1] (numeric) = 1.12574633884673 " "
absolute error = 6.26165785888588300000000000000E-14 " "
relative error = 5.5622280462402260000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5069999999999992 " "
y1[1] (analytic) = 2.4855568204913547 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.131281887151729000E-3 " "
relative error = 0.24667639205044098 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.125794890157735 " "
y2[1] (numeric) = 1.125794890157668 " "
absolute error = 6.70574706873594600000000000000E-14 " "
relative error = 5.956455414179757000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5070999999999992 " "
y1[1] (analytic) = 2.4856442385744093 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.218699970206298000E-3 " "
relative error = 0.2501846351822619 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1258434502107288 " "
y2[1] (numeric) = 1.1258434502106567 " "
absolute error = 7.21644966006351800000000000000E-14 " "
relative error = 6.4098162659406910000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5071999999999992 " "
y1[1] (analytic) = 2.485731651801021 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.306113196818064000E-3 " "
relative error = 0.25369243668153035 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1258920190052881 " "
y2[1] (numeric) = 1.1258920190052106 " "
absolute error = 7.74935671188359300000000000000E-14 " "
relative error = 6.882859618038731000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5072999999999992 " "
y1[1] (analytic) = 2.4858190601703165 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.3935215661135030000E-3 " "
relative error = 0.2571997965803452 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1259405965409273 " "
y2[1] (numeric) = 1.1259405965408442 " "
absolute error = 8.30446822419617100000000000000E-14 " "
relative error = 7.375582912374639000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5073999999999992 " "
y1[1] (analytic) = 2.4859064636814217 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.480925077218647000E-3 " "
relative error = 0.2607067149107828 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1259891828171602 " "
y2[1] (numeric) = 1.1259891828170714 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 7.887983590374765000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5074999999999992 " "
y1[1] (analytic) = 2.485993862333462 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.568323729259085000E-3 " "
relative error = 0.26421319170489704 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1260377778335013 " "
y2[1] (numeric) = 1.1260377778334065 " "
absolute error = 9.48130463029883700000000000000E-14 " "
relative error = 8.42005909299143000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5075999999999992 " "
y1[1] (analytic) = 2.4860812561255634 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.655717521360405000E-3 " "
relative error = 0.26771922699473694 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1260863815894648 " "
y2[1] (numeric) = 1.1260863815893636 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 8.991525117540019000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5076999999999992 " "
y1[1] (analytic) = 2.4861686450568525 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.743106452649528000E-3 " "
relative error = 0.27122482081240024 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1261349940845644 " "
y2[1] (numeric) = 1.1261349940844563 " "
absolute error = 1.08135722598490250000000000000E-13 " "
relative error = 9.602376550459106000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5077999999999991 " "
y1[1] (analytic) = 2.4862560291264555 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.830490522252486000E-3 " "
relative error = 0.27472997318994435 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1261836153183142 " "
y2[1] (numeric) = 1.1261836153181988 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 1.025260827723734600000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5078999999999991 " "
y1[1] (analytic) = 2.486343408333498 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 6.917869729294868000E-3 " "
relative error = 0.278234684159404 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1262322452902278 " "
y2[1] (numeric) = 1.1262322452901048 " "
absolute error = 1.23012711128467340000000000000E-13 " "
relative error = 1.092249947938288800000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5079999999999991 " "
y1[1] (analytic) = 2.486430782677106 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.0052440729031500000E-3 " "
relative error = 0.2817389537528448 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1262808839998188 " "
y2[1] (numeric) = 1.1262808839996878 " "
absolute error = 1.31006316905768470000000000000E-13 " "
relative error = 1.163176244637297200000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5080999999999991 " "
y1[1] (analytic) = 2.4865181521564064 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.092613552203364000E-3 " "
relative error = 0.28524278200230996 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.126329531446601 " "
y2[1] (numeric) = 1.1263295314464616 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 1.23803920610893300000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5081999999999991 " "
y1[1] (analytic) = 2.4866055167705254 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.179978166322432000E-3 " "
relative error = 0.2887461689398733 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1263781876300878 " "
y2[1] (numeric) = 1.1263781876299397 " "
absolute error = 1.48103751484995880000000000000E-13 " "
relative error = 1.314867005695554100000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5082999999999991 " "
y1[1] (analytic) = 2.4866928765185894 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.267337914386385000E-3 " "
relative error = 0.29224911459756847 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.126426852549793 " "
y2[1] (numeric) = 1.1264268525496355 " "
absolute error = 1.5742962489184720000000000000E-13 " "
relative error = 1.397601846364792000000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5083999999999991 " "
y1[1] (analytic) = 2.4867802313997243 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.354692795521256000E-3 " "
relative error = 0.29575161900742425 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1264755262052293 " "
y2[1] (numeric) = 1.1264755262050623 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 1.48230067160111900000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5084999999999991 " "
y1[1] (analytic) = 2.486867581413057 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.442042808853966000E-3 " "
relative error = 0.2992536822015003 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1265242085959106 " "
y2[1] (numeric) = 1.1265242085957332 " "
absolute error = 1.77413639335100020000000000000E-13 " "
relative error = 1.574876402844700200000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.508599999999999 " "
y1[1] (analytic) = 2.486954926557714 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.529387953510991000E-3 " "
relative error = 0.30275530421183366 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1265728997213498 " "
y2[1] (numeric) = 1.1265728997211617 " "
absolute error = 1.88071780371501520000000000000E-13 " "
relative error = 1.669415094380663800000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.508699999999999 " "
y1[1] (analytic) = 2.4870422668328214 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.6167282286183640000E-3 " "
relative error = 0.30625648507043884 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1266215995810598 " "
y2[1] (numeric) = 1.1266215995808606 " "
absolute error = 1.99174010617753080000000000000E-13 " "
relative error = 1.76788737844025880000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.508799999999999 " "
y1[1] (analytic) = 2.4871296022375065 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.7040636333034480000E-3 " "
relative error = 0.30975722480937906 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.126670308174554 " "
y2[1] (numeric) = 1.126670308174343 " "
absolute error = 2.10942374678779740000000000000E-13 " "
relative error = 1.872263546383425600000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.508899999999999 " "
y1[1] (analytic) = 2.4872169327708957 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.791394166692722000E-3 " "
relative error = 0.3132575234606771 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.126719025501345 " "
y2[1] (numeric) = 1.1267190255011217 " "
absolute error = 2.2337687255458150000000000000E-13 " "
relative error = 1.98254283010076700000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.508999999999999 " "
y1[1] (analytic) = 2.4873042584321152 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.878719827912217000E-3 " "
relative error = 0.31675738105633316 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1267677515609456 " "
y2[1] (numeric) = 1.1267677515607095 " "
absolute error = 2.3603341503530828000000000000E-13 " "
relative error = 2.094783194747312000000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.509099999999999 " "
y1[1] (analytic) = 2.4873915792202923 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 7.966040616089298000E-3 " "
relative error = 0.32025679762839615 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.126816486352869 " "
y2[1] (numeric) = 1.1268164863526193 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 2.214896027511425400000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.509199999999999 " "
y1[1] (analytic) = 2.4874788951345534 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.053356530350442000E-3 " "
relative error = 0.3237557732088745 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1268652298766273 " "
y2[1] (numeric) = 1.1268652298763637 " "
absolute error = 2.63566946046012160000000000000E-13 " "
relative error = 2.338939378534807300000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.509299999999999 " "
y1[1] (analytic) = 2.487566206174026 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.140667569823012000E-3 " "
relative error = 0.3272543078298076 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1269139821317333 " "
y2[1] (numeric) = 1.126913982131455 " "
absolute error = 2.78221889971064230000000000000E-13 " "
relative error = 2.468883112487114400000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.509399999999999 " "
y1[1] (analytic) = 2.487653512337836 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.227973733633043000E-3 " "
relative error = 0.33075240152317653 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1269627431176996 " "
y2[1] (numeric) = 1.126962743117406 " "
absolute error = 2.9354296771089140000000000000E-13 " "
relative error = 2.604726460599894300000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.509499999999999 " "
y1[1] (analytic) = 2.4877408136251113 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.315275020908341000E-3 " "
relative error = 0.33425005432102894 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1270115128340383 " "
y2[1] (numeric) = 1.1270115128337288 " "
absolute error = 3.09530179265493640000000000000E-13 " "
relative error = 2.746468653963737300000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5095999999999989 " "
y1[1] (analytic) = 2.4878281100349784 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.402571430775385000E-3 " "
relative error = 0.33774726625535423 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1270602912802619 " "
y2[1] (numeric) = 1.1270602912799357 " "
absolute error = 3.261835246348710000000000000E-13 " "
relative error = 2.894108923528388000000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5096999999999989 " "
y1[1] (analytic) = 2.487915401566564 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.489862962361094000E-3 " "
relative error = 0.34124403735815484 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1271090784558826 " "
y2[1] (numeric) = 1.127109078455539 " "
absolute error = 3.43503003819023430000000000000E-13 " "
relative error = 3.047646500102863500000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5097999999999989 " "
y1[1] (analytic) = 2.4880026882189963 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.577149614793278000E-3 " "
relative error = 0.3447403676614641 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1271578743604125 " "
y2[1] (numeric) = 1.127157874360051 " "
absolute error = 3.61488616817950970000000000000E-13 " "
relative error = 3.207080614355569700000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5098999999999989 " "
y1[1] (analytic) = 2.4880899699914014 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.664431387198412000E-3 " "
relative error = 0.34823625719725704 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.127206678993364 " "
y2[1] (numeric) = 1.1272066789929833 " "
absolute error = 3.80584452841503660000000000000E-13 " "
relative error = 3.37635022870321600000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.5099999999999989 " "
y1[1] (analytic) = 2.4881772468829064 " "
y1[1] (numeric) = 2.479425538604203 " "
absolute error = 8.751708278703418000E-3 " "
relative error = 0.35173170599752185 "%"
h = 1.0000E-4 " "
y2[1] (analytic) = 1.1272554923542482 " "
y2[1] (numeric) = 1.127255492353848 " "
absolute error = 4.0012437807490640000000000000E-13 " "
relative error = 3.549544719797776400000000000E-11 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff(y1,x,1) = diff(y2,x,5);"
"diff(y2,x,1) = y1 - 2.0;"
Iterations = 100
"Total Elapsed Time "= 6 Minutes 12 Seconds
"Elapsed Time(since restart) "= 6 Minutes 12 Seconds
"Expected Time Remaining "= 4 Days 1 Hours 18 Minutes 22 Seconds
"Optimized Time Remaining "= 4 Days 1 Hours 13 Minutes 44 Seconds
"Time to Timeout "= 8 Minutes 47 Seconds
Percent Done = 0.1063157894736725 "%"
(%o56) true
(%o56) diffeq.max